A discontinuous Petrov-Galerkin method for compressible Navier-Stokes equations in three dimensions. (15th November 2021)

• Record Type: Journal Article
• Authors: Rachowicz, Waldemar; Zdunek, Adam; Cecot, Witold
• Is Part Of: Computers & mathematics with applications. Volume 102(2021)
• Page Start: 113
• Page End: 136
• Publication Date: 2021-11-15
• Subjects: Finite element method -- Compressible Navier-Stokes equations -- Discontinuous Petrov-Galerkin -- h-adaptivity -- Error estimation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.010
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Application of a Discontinuous Petrov-Galerkin (DPG) method for simulation of compressible viscous flows in three dimensions is presented. The approach enables construction of stable schemes for problems with a small perturbation parameter. The main idea of the method is a weak formulation with a relaxed interelement continuity of the solution. The formulation satisfies the inf-sup condition with the stability constant independent of the small perturbation parameter, which here is the viscosity constant for the compressible Navier-Stokes equations. The DPG discrete formulation uses the specially designed so-called optimal test functions. They do not compromise the inf-sup stability of the continuous formulation. DPG does not use any artificial dissipation for the compressible Navier-Stokes equations. Being a residual minimization method it has got a built-in a posteriori error estimation which allows for mesh adaptivity leading to resolving reliable viscous fluxes, the major difficult task in simulations of viscous flows. We illustrate the method with a few steady state laminar solutions.